Anisotropic Neumann problems in Sobolev spaces with variable exponent

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

“…( see [9], [12]) The functionals Ψ(·, ·) and Φ(·, ·) are well defined on X. In addition, Ψ(·, ·) and Φ(·, ·) is of class C 1 (X, R) and…”

“…It is no surprising that there exist previous works treating problems with same operator, to give some examples, we refer the reader to [8,12,13] where the authors were concerned with Dirichlet problems. Our work is focused on a Neumann problem, we refer the reader to [1,9].…”

Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

“…The authors use minimization technics used in [2] or [3] (see also [4,5]) to prove the existence and uniqueness of entropy solution.…”

“…The Robin type boundary conditions in the variable exponents setting are new and interesting problems and were for the first time studied by Boureanu and Radulescu in [3]. The main difficulty for the study of problem in [3] was the definition of an admissible space of solutions.…”

“…The main difficulty for the study of problem in [3] was the definition of an admissible space of solutions. The authors defined the appropriate space and obtained its properties on Ω.…”